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Endpoint estimates for one-dimensional oscillatory integral operator
| Content Provider | Semantic Scholar |
|---|---|
| Author | Xiao, Lechao |
| Copyright Year | 2016 |
| Abstract | The one-dimensional oscillatory integral operator associated to a real analytic phase $S$ is given by $ T_\lambda f(x) =\int_{-\infty}^\infty e^{i\lambda S(x,y)} \chi(x,y) f(y) dy. $ In this paper, we obtain a complete characterization for the mapping properties of $T_\lambda $ on $L^p(\mathbb R)$ spaces, namely we prove that $\|T_\lambda\|_p \lesssim |\lambda|^{-\alpha}\|f\|_p$ for some $\alpha>0$ if and only if the point $(\frac 1 {\alpha p} , \frac 1 {\alpha p'})$ lies in the reduced Newton polygon of $S$, and this estimate is sharp if and only if it lies on the reduced Newton diagram. |
| Starting Page | 255 |
| Ending Page | 291 |
| Page Count | 37 |
| File Format | PDF HTM / HTML |
| DOI | 10.1016/j.aim.2017.06.007 |
| Alternate Webpage(s) | https://arxiv.org/pdf/1602.05663v2.pdf |
| Alternate Webpage(s) | https://www.math.upenn.edu/~xle/Endpoint%20Estimates.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
